On axisymmetrical boundary problem of unsteady motion of micropolar fluid in the half-space

The aim of this paper is developing an exact solution for the problem of axisymmetrical flow of unsteady motion of micropolar fluid in the half-space when the shear stresses are given on the boundary. The Laplace-Hankel transform technique is used to solve this problem. Some physical quantities such as velocities, pressure and microrotations are obtained and illustrated numerically.

Tip Loss Correction for Actuator/Navier–Stokes Computations

A new tip loss correction, initially developed for 1D Blade Element/Momentum (BEM) computations (submitted to Wind Energy), is now extended to 2D Actuator Disc/Navier–Stokes (AD/NS) computations and 3D Actuator Line/Navier–Stokes (AL/NS) computations. In the paper, it is shown that the tip loss correction is an important and necessary step for actuator/Navier–Stokes models. Computed results are compared to experimental data and to results from BEM computations using the new tip correction as well as the original one of Glauert (Aerodynamic Theory, Dover, New York, Chap. VII, Div. L, pp. 251–268). From the results it is concluded that the tip loss correction has been correctly employed in the Navier–Stokes based actuator models. The results also demonstrate that the difference between actuator line and actuator disk-based models may increase, especially for flows at a low tip speed ratio. Since the flows at a low tip speed ratio are too far to be considered as axisymmetrical flows, the actuator disk models that are based on axisymmetrical flow behaviors may not be valid.

A Summary of Developments of the Mean-Streamline Method in China

The mean-streamline method (MSLM) proposed by Wu more than 30 years ago has been further developed in many ways in China since the fifties. Major progress in this method is summarized here. This progress includes: a completely analytical solution of the inverse problem which is extremely quick and more accurate than the original solution, the extension of MSLM to the axisymmetrical flow channels, the extension of the calculation range to transonic flow and nonisentropic flow, the estimation of applicable limits of MSLM, the improvement of MSLM with higher order derivatives, and the development of practical computer programs. The comparison of the calculation results with the experimental data is good, and the method has been widely applied in China with good success.

Basic Flow Analyses Used in the Study of Broad-Band Noise in Compressors

The propagation of sound in a moving compressible fluid displays interesting features which are important in the problem of noise generation in compressors. Without considering the discrete frequency noise generated by interacting rotating blades and stationary parts, a perturbation method applied to the equations of flow motion in an idealized continuous medium leads to an equation of density waves propagation in a nonhomogeneous moving fluid. The right-hand side is considered as describing distributed noise sources which involve velocity fluctuations. On the left-hand side there appears a negative diffusive effect due to a negative divergence of the velocity field, which downstream entails a streamwise amplification of the intensity of the sound generated upstream. Further, there is a dispersive effect entailing, for a given wave number, a group velocity which in a simple example is shown to be larger than the phase velocity and to become imaginary for a velocity divergence sufficiently high in absolute value. This, together with the amplification effect, may explain the relative importance of the high frequency band in the actual noise spectra of compressors. An attempt at determining the coefficients of the acoustical equation for compressors is made in the schematic Beltrami-Gromeka case of a helicoidal axisymmetrical flow. With simplified assumptions on the behavior of density, depending either solely on the axial coordinate or only on the radial one, both types of axial and radial compressors are considered simultaneously and the method of analytical solution applied. It is emphasized that this treatment is restricted to the mechanical aspect of the broad-band noise generation.